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Title: | On the inverse of the adjacency matrix of a graph |
Authors: | Farrugia, Alexander Gauci, John Baptist Sciriha, Irene |
Keywords: | Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 2013 |
Publisher: | De Gruyter Open |
Citation: | Farrugia, A., Gauci, J. B., & Sciriha, I. (2013). On the inverse of the adjacency matrix of a graph. Special Matrices, 28-41. |
Abstract: | A real symmetric matrix G with zero diagonal encodes the adjacencies of the vertices of a graph G with weighted edges and no loops. A graph associated with a n × n non–singular matrix with zero entries on the diagonal such that all its (n − 1) × (n − 1) principal submatrices are singular is said to be a NSSD. We show that the class of NSSDs is closed under taking the inverse of G. We present results on the nullities of one– and two–vertex deleted subgraphs of a NSSD. It is shown that a necessary and sufficient condition for two–vertex deleted subgraphs of G and of the graph (G−1) associated with G−1 to remain NSSDs is that the submatrices belonging to them, derived from G and G−1, are inverses. Moreover, an algorithm yielding what we term plain NSSDs is presented. This algorithm can be used to determine if a graph G with a terminal vertex is not a NSSD |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28173 |
Appears in Collections: | Scholarly Works - FacSciMat Scholarly Works - JCMath |
Files in This Item:
File | Description | Size | Format | |
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On_the_inverse_of_the_adjacency_matrix_of_a_graph_2013.pdf | 1.11 MB | Adobe PDF | View/Open |
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